Updating with Belief Functions, Ordinal Conditioning Functions and Possibility Measures
This work addresses foundational issues in uncertainty representation for AI and decision-making, but it appears incremental as it reinterprets and connects existing theories.
The paper tackles the problem of updating uncertainty measures when new uncertain information becomes available, across frameworks like evidence theory, possibility theory, and Spohn's theory, by introducing analogues of Jeffrey's rule and contrasting updating rules.
This paper discusses how a measure of uncertainty representing a state of knowledge can be updated when a new information, which may be pervaded with uncertainty, becomes available. This problem is considered in various framework, namely: Shafer's evidence theory, Zadeh's possibility theory, Spohn's theory of epistemic states. In the two first cases, analogues of Jeffrey's rule of conditioning are introduced and discussed. The relations between Spohn's model and possibility theory are emphasized and Spohn's updating rule is contrasted with the Jeffrey-like rule of conditioning in possibility theory. Recent results by Shenoy on the combination of ordinal conditional functions are reinterpreted in the language of possibility theory. It is shown that Shenoy's combination rule has a well-known possibilistic counterpart.